The paper considers a problem of optimal control of a linear system wi
th the parameters dependent on the states of a Markov chain. The cost
criterion is quadratic in the controls and states of the system. The c
riterion parameters also depend on the states of the Markov chain. Two
models of observation of the Markov chain are adopted - delay for one
step and no delay. It is shown that under appropriate mean square det
ectability and stabilizability conditions the infinite horizon optimal
control problem for the general case of Markovian jump linear quadrat
ic systems has a unique mean square stabilizing solution. Necessary an
d sufficient conditions are gives to determine if a system is mean squ
are stabilizable.